The strain-rate dependence of the Hall-Petch effect in two austenitic stainless steels with different stacking fault energies

The strain-rate dependence of the Hall-Petch effect in two austenitic stainless steels with different stacking fault energies

Accepted Manuscript The strain-rate dependence of the Hall-Petch effect in two austenitic stainless steels with different stacking fault energies Serg...

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Accepted Manuscript The strain-rate dependence of the Hall-Petch effect in two austenitic stainless steels with different stacking fault energies Sergey V. Astafurov, Galina G. Maier, Evgenii V. Melnikov, Valentina A. Moskvina, Marina Yu. Panchenko, Elena G. Astafurova PII:

S0921-5093(19)30549-0

DOI:

https://doi.org/10.1016/j.msea.2019.04.076

Reference:

MSA 37826

To appear in:

Materials Science & Engineering A

Received Date: 20 February 2019 Revised Date:

17 April 2019

Accepted Date: 18 April 2019

Please cite this article as: S.V. Astafurov, G.G. Maier, E.V. Melnikov, V.A. Moskvina, M.Y. Panchenko, E.G. Astafurova, The strain-rate dependence of the Hall-Petch effect in two austenitic stainless steels with different stacking fault energies, Materials Science & Engineering A (2019), doi: https:// doi.org/10.1016/j.msea.2019.04.076. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT The strain-rate dependence of the Hall-Petch effect in two austenitic stainless steels with different stacking fault energies Sergey V. Astafurov, Galina G. Maier, Evgenii V. Melnikov, Valentina A. Moskvina,

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Marina Yu. Panchenko, Elena G. Astafurova Institute of Strength Physics and Materials Science SB RAS, Akademicheskii ave., 2/4,

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634055, Tomsk, Russia

Abstract. Using thermal-mechanical treatments, specimens with different grain sizes

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were produced for two Cr-Ni-based austenitic stainless steels with different stacking fault energies (analogues of AISI 316L and AISI 321 steels). The effect of strain-rate on the tensile deformation behavior and strength properties was evaluated for these steels. In given grain size interval, (3–73)µm for 316 steel and (0.2–32)µm for 321 steel, the .

varies with grain size D in accordance with Hall-Petch relationship

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yield strength

σ0.2 =σ0 +kHP D-1⁄2 . The Hall-Petch coefficient kHP depends on steel composition (stacking fault energy) and possesses higher value for 321 steel as compared to 316

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steel. Increase in strain-rate in the interval of 1.0×10-4 s-1 to 1.0×10-2 s-1 causes growth in stress σ0, but weakly changes coefficient kHP in Hall-Petch relationship: 322-327

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MPa×m0.5 for 316 steel and 404-413 MPa×m0.5 for 321 steel. The strain-rate dependence of the constants in Hall-Petch relationship was discussed in terms of deformation mechanism and dislocation arrangement in both steels.

Keywords: austenitic stainless steel, Hall-Petch relationship, strain rate, grain size, thermal-mechanical treatment

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ACCEPTED MANUSCRIPT 1. Introduction A good combination of mechanical, technological and functional characteristics of austenitic stainless steels (SS) determines their widespread application in various

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branches of modern industry [1-3]. Among the advantages of this class of steels are high corrosion resistance, weldability, relatively high ductility, etc. [4]. At the same time, the main disadvantage of modern commercial austenitic SSs, which significantly limits the

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possibility of their use as structural materials for critical elements of machines and mechanisms, is rather low values of a yield strength [1,4].

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The most promising way to increase strength properties of austenitic SSs is to reduce a grain size using various methods of plastic deformation and thermalmechanical treatments [1,2,4–6]. From the point of view of potential industrial applications, the most convenient techniques are the methods of plastic deformation and

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different combinations of deformation and heat treatments, which allow processing large volumes of material [2]. In this case, multiple cold rolling is common and one of the most available methods. Depending on the thermal-mechanical treatment regime,

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temperature and duration of postdeformation annealing, the grain size can be varied in a wide range of values [1]. Wherein, numerous experimental data show that the increase

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in yield stress is accurately described by the Hall-Petch relationship [1,2,4-7]. Besides the refinement of grain size and deformation-induced defects, the

physical reason for increasing the strength characteristics of austenitic stainless steels processed via plastic deformation is the formation of strain-induced martensite [4,5,8]. The consequence of this fact is a significant decrease in ductility of the SSs after treatment. This problem could be solved by using post-deformation annealing, which allows to transform the resulting martensitic phase to nano- or ultrafine austenite [1,3-

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ACCEPTED MANUSCRIPT 6]. The formation of nano- or ultrafine-grained austenitic stainless steels as a result of the combination of multiple cold rolling and postdeformation annealing leads to substantial increase in strength characteristics of the steels without a significant loss of

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ductility. In this regard, this technology can be considered as an effective way to form a small (submicron) grain size [9]. Thus, a combination of cold rolling and postdeformation annealing can produce a material with high strength characteristics and

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ductility [5,10].

Analysis of the current literature data shows that a large number of papers

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related to the study of the effect of grain size on the mechanical properties of austenitic stainless steels subjected to plastic deformation with subsequent post-deformation annealing are devoted to widely used in industry AISI 3XX-type steels and their analogues. Some literary data for SSs are summarized in Table 1. In relation to the

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construction of the Hall-Petch relationship, the area of this relationship for austenitic stainless steels is investigated rather weakly as compared to pure metals. Moreover, such aspects as the strain rate (ε), stacking fault energy (SFE) and deformation

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mechanism are rarely discussed in existing studies on the determination of the values of the Hall-Petch coefficient (kHP) for austenitic stainless steels. This is due to the

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assumption that the strain rate (in the static loading range) and SFE do not fundamentally change their deformation mechanisms in the early plastic deformation regime (at low strain, near the yield strength). In fcc alloys, an increase in the strain rate or decrease in SFE can significantly

influence the development of such deformation mechanism as mechanical twinning or lead to a change in the dislocation arrangement in slip-associated deformation in steels [20,21]. For this reason, the question of the effect of strain rate and SFE on the

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ACCEPTED MANUSCRIPT parameters of the Hall-Petch relationship becomes relevant and requires detailed study. This paper is devoted to overall investigation of the influence of strain rate and grain size on mechanical properties and Hall-Petch relationship parameters of AISI

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316L-type and AISI 321-type austenitic stainless steels possessing different stacking fault energies.

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2. Materials and Methods

Two austenitic stainless steels were considered in the paper. These steels, 316SS

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and 321SS, are Russian analogous of AISI316L and AISI321 steels respectively. Proper chemical compositions of the investigated steels are shown in Table 2. Original steel bars were water-quenched after 1-hour exposure at 1050-1100°С (solid solution treatment, SST). For each type of steel, a set of billets was prepared.

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Billets were subjected to thermal-mechanical treatment using special scheme: multiple cold rolling (CR) at room temperature (RT) to a total cumulative reduction of 80% with following annealing in the temperature interval of 650-1050°С and water-cooling. All

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thermal treatments were carried out in inert gas atmosphere. Detailed data about thermal-mechanical treatments and obtained grain sizes are summarized in Table 3.

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For static tensile tests, proportional flat dumbbell-shaped specimens were cut from the billets. The gauge sections of the tensile specimens were equal to 20.0×2.7×1.2 (mm). After mechanical grinding, an electrolytic polishing of the specimens in a supersaturated solution of chromium anhydride (CrO3) in phosphoric acid (H3PO4) was performed. Static uniaxial tension tests were carried out at RT with three initial strain rates of 1.0×10–4 s–1, 1.0×10–3 s–1 and 1.0×10–2 s–1 using LFM-125 testing machine (Walter +

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ACCEPTED MANUSCRIPT Bai AG, Switzerland). Five specimens were tensile tested for each treatment regime. The grain size of the specimens was determined using the images obtained by the methods of light microscopy (LM, microscope Altami MET 1C), scanning electron

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microscopy (a Quanta 200 3D microscope equipped with an electron back scattered diffraction (EBSD) unit) and transmission electron microscopy (TEM, JEOL JEM2100). The visualization of EBSD data was performed with the TSL OIM Analysis 6.2

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software, no cleaning or coarsening of the EBSD-maps was used. The average grain sizes (excluding twin boundaries) were calculated with linear intercept method.

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The magnetophase analysis of the specimens (determination of the volume fraction of ferrite) was carried out using a multifunction vortex-current instrument MVP-2M (Kropus, Russia). The accuracy of determining the volume fraction of ferrite was 0.1%.

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Investigation of the microstructure (dislocation arrangement and deformation mechanism) has been done by means of conventional TEM methods. Specimens were deformed to plastic strain of 5% and then were unloaded. Thin foil preparation of the

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deformed specimens for TEM studies were performed at temperature of -8 oC. Indexing of selected area electron diffraction (SAED) patterns was performed as detailed

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elsewhere [22]. Using bright-field TEM images, the values of stacking fault energy of the steels was estimated by measuring the extended threefold dislocation nodes [22].

3. Results and Discussion 3.1. Initial structure of 316 SS and 321 SS after thermal-mechanical processing After thermal-mechanical treatments listed in Table 3, all specimens possess a predominantly austenitic structure as it was revealed using TEM, EBSD data and

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ACCEPTED MANUSCRIPT magnetophase analysis. Data in Table 3 suggests that thermal-mechanical treatments result in formation of steel specimens with austenitic, mainly grain, structure of different scales. The range of grain sizes varies from 0.2 µm to 32 µm for 321 steel and

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from 3 µm to 73 µm for 316 steel. Data on grain size in Table 3 concern grain size of the steels excluding coherent boundaries of anneal twins. According to R.A. Varin and K.J. Kurzydlowski [14], twin boundaries do not influence grain boundary strengthening

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parameter kHP in Hall-Petch relationship. The characteristic LM, TEM and EBSD images for some fine-grained and coarse-grained specimens are shown in Figures 1 a,c

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and Figures 2 a,c,e.

High concentration of Ni stabilizes austenitic structure in 316SS. CR-processing does not influence phase composition of this steel, but deformation is accompanied with a substantial refinement of the austenitic structure and with accumulation of

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deformation-induced defects of a crystal lattice [23,24]. During post-deformation annealing, grain structure with large number of annealing twins forms as a result of recrystallization processes in severely-deformed austenite (Fig. 1 a,c). Variations in

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annealing temperature and in exposure during annealing allow producing rather wide range of grain sizes in 316SS (Table 3).

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Chemical composition of the 321SS strongly affects deformation mechanisms in comparison with 316SS. After CR-processing, a large volume fraction of deformationinduced α’-martensite forms [23]. Post-deformation annealing according to regimes in Table 3 provides a reversion of α’-martensite to γ-phase (Fig. 2 a,c,e). Nevertheless, the small volume fraction of bcc-Fe phase is still present (Table 4). Therefore, the γ→α’ reversion is not completed after post-deformation annealing. In accordance with K. Tomimura et al. [25], high Cr concentration (≈17 mass.%) could be responsible for

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ACCEPTED MANUSCRIPT incomplete reverse transformation in cold-rolled 321SS under annealing at temperatures higher 600°C. But in this case, tempered α’-phase particles are rather large and are located in three- or four-grain junctions [25]. They could suppress austenite grain

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growth during annealing but would hardly affect the yield strength of the 321SS because of low volume fraction (Table 4). The grain size variations vs. annealing temperature and reverse transformation behavior in 321SS correlate with data for Cr-Ni

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steels in [25].

3.2. Tensile properties of 316 SS and 321 SS at different strain rates

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Figures 1 b, 1d, 2 b, 2d and 2f show “engineering stress vs engineering strain” curves for 316 SS and 321 SS with different grain sizes for different strain rates. Analysis of the curves in Figures 1 and 2 showed that the coarse-grained specimens of the investigated steels are characterized by high ductility (ultimate strains is 63-70%)

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and low values of the yield strength (σ0.2) and ultimate tensile strength (σUTS) (Table 4). A decrease in the grain size leads to an increase in σUTS (up to 25%) and σ0.2 (up to 5 times) and is also accompanied with a decrease in the elongation of specimens from

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≈70% in the coarse-grained state to 6-8% in fine-grained one. Irrespective of grain size, the increase in strain rate from 1.0×10-4 s-1 to 1.0×10-2 s-1 leads to increase in the

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strength characteristics of both steels. Data on the effect of grain size and strain rate on the mechanical properties of 316 SS and 321 SS specimens are summarized in Table 4. 3.3.The effect of strain rate and stacking-fault energy on parameters of Hall-Petch relationship

Data in Tables 3 and 4 allow to perform an analysis of a change in σ0.2-value with variation in the grain size D-1/2 according to the Hall-Petch relationship [26,27]:

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ACCEPTED MANUSCRIPT .

=

+

.

(1)

here σ0 – yield stress in single crystal (friction stress), D – grain size, kHP – Hall-Petch

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coefficient, which is the grain boundary strengthening parameter. The graphs for linear regression analysis based on the data in Tables 3 and 4 for both steels depending on strain rate are shown in Figure 3 a, b. The experimental data fit the Hall-Petch

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relationship (1) with high degree of accuracy (the correlation coefficients R are close to 1, Table 5). Values of σ0 and Hall-Petch coefficients for assumed strain rates interval

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(1.0×10-2-1.0×10-4) s-1 are summarized in Table 5.

Hall-Petch equation predicts the behavior of both steels and measured coefficients kHP correlate adequately with some data of other authors (Table 1). For CrNi steels, in which different grain sizes were produced with combination of pre-

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deformation and high-temperature heat treatments or high-temperature plastic deformation, kHP-values reported by other authors lie in rather narrow range 280-410 MPa× µm0,5 [1,8,13,14,17,19] (Table 1). This kHP-range adequately covers grain size

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effect for steels with grain size range of micrometers to hundreds of micrometers with equiaxed structure and low density of defects (present results fit this range accurately).

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A deviation from this kHP-values was reported by Z. Wang et al. [16] for additively built 304 steel with coarse-grained structure (695 MPa × µm0,5), which can be ascribed to substantial nonequiaxiality of grain structure. Some regular increase in Hall-Petch coefficients were also reported for Cr-Ni steels for grain sizes including ultrafinegrained range – kHP reaches 400-470 MPa× µm0,5 [2,17,18]. But controversial data kHP=220 MPa× µm0,5 was found for 316 steel with grain(subgrain) size of 0.04-0.1 µm. This discrepancy could arise due to differences in processing parameters of the steels

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ACCEPTED MANUSCRIPT and peculiarities of grain(subgrain) structure (fraction and distribution of defects, boundaries, subboundaries). Additional careful researches are needed for clarification of Hall-Petch coefficients for ultrafine-grained steels. K.Kako with coauthors [19] reported

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the increase in kHP-coefficient from 439 MPa× µm 0,5 to 537 MPa× µm 0,5 by alloying of Fe-18Cr-14Ni steel with 0.09 mass % of nitrogen. The effect of substitutional alloying is not so influential, but also exists [19].

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The extrapolated stress σ0 is strain-rate sensitive value (Table 5). It increases in 15% and 32% respectively for 316SS and 321SS with increase in strain rate from

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1.0×10-4 s-1 up to 1.0×10-2 s-1 (Table 5). This value is usually associated with the friction stress required for propagation of dislocations in crystal lattice. Friction stress includes contributions from solutes and ‘forest’ dislocations, it usually corresponds to the stress for start of plastic flow in single crystal oriented for multiple slip. For 3XX-type steel

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there are limited data on the yield stress in single crystals, all of them are in good correlation with data in Table 5. σ0≈200MPa was measured in work of I. Kireeva and Yu. Chumlyakov [28] for <111>-oriented single crystals of 316-type steel tensile tested

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at room temperature and 5×10-4 s-1 (multiple slip was observed in TEM images). I. Karaman et al. [29] reported σ0 ≈ 190MPa for <001>-oriented and σ0 ≈ 290MPa for

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<111>-oriented single crystals of 316L steel deformed in room temperature tension at strain rate 5×10-5 s-1 (slip-associated deformation was observed in both orientations). Using strain-rate dependence of the σ0-value in Table 5 one could estimate an

activation volume V for interaction of dislocations with solutes and ‘forest’ dislocations using Gibbs approach [30]:

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=



=

ln



(2)

= 1.38×10-23 JK-1 is the Boltzman constant, T is the temperature, M=3.06 is

the Taylor factor,

1,

2

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where

ln

– strain rates and σ1(τ1), σ2(τ2) – associated normal (shear)

stresses. The activation volumes, 92b3 for 316SS and 106b3 for 321SS respectively

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(here b is Burgers vector value). These values correspond the lower limit peculiar for thermally-activated movement of dislocations in crystal lattice of coarse-grained metals

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with ‘forest’ dislocations at low strain (100-1000 b3) [31]. For 321SS and 316SS, the difference in total substitutional concentrations Csub=30.1 mass.% and Csub=35.1 mass.% could determine the variation in absolute σ0-values but provides close activation parameters at low strain. The effect of solute atoms on σ0-value was described, for

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instance, in works [19,32]. Substitutional concentrations are values of one-order in both steels, but interstitial content (carbon concentration is c=0.1 mass. %) in 321SS is one order higher than that in 316SS (c=0.01 mass. %). Taking into account carbon

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concentration, the activation volume for 321SS should be about 4.5 times lower than that for 316SS following the dependence V~b3c-2/3 [33] and assuming deformation by

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dislocation slip with Burgers vector b=a/2<110>. At the same time, estimated activation volumes for the steels are close to each other. Relative to the strain-rate dependence of the σ0-value, mentioned above facts could testify either slip-associated overcoming of alloying atoms or ‘forest’ dislocations. Independently on mentioned above factors, thermally activated short range interaction of dislocations with solute atoms and ‘forest’ dislocations is strain-rate dependent value and could be described in general form [33,34]:

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=

+

U kT γ − ln " $ (3) V V γ

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where τf – athermal component of the stress, U – activation energy, γ – constant, γ – shear strain rate (which is proportional to ). The plots of experimental σ0 vs. ln

%

for

both steels are shown in Figure 3c. These plots clearly show that equation (3) describes

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the experimentally observed strain-rate dependence of the friction stresses with high

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accuracy.

From the analysis of data in Table 5 and Figure 3 it can be concluded that the Hall-Petch coefficient kHP is almost independent (or slowly increases up to 2-3%) on the strain rate in the interval of 1.0×10-4 s-1 to 1.0×10-2 s-1. The value of Hall-Petch coefficient (kHP) describes grain-boundary barrier effect [27]. As it follows from works

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[35,36], this coefficient kHP can be expressed via relation:

.

(4)

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= 3 '()* + ,-⁄2/ 0

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where M и ms – Taylor and Sachs orientation factors, G – shear modulus, b – Burgers vector, / = 2'1 − 20⁄'2 − 20, ν – Poisson coefficient, and

с

– concentrated shear

stress, which is need for operation of dislocation source near the grain boundary. For the 321SS and 316SS, the values of elastic modulus and Poisson coefficient

are almost independent on strain-rate in the interval 1.0×10-4 s-1 to 1.0×10-2 s-1. This, in particular, is seen from flow curves in Figures 1 and 2, where increase in strain-rate does not change the slope of the stress-strain curved in elastic deformation regime. The

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ACCEPTED MANUSCRIPT с

stress and Burgers vector

444

– shear stress for start of

444 -stress

depends on strain rate as

values, which can be directly dependent on strain rate, are b. Armstrong and Panin [37,38] related the

с -value

stage III of strain hardening. In their consideration,

to the

=

5 678'−9 0 (5) )

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444

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[38]:

where T – absolute temperature, B and β – experimental constants, which vary with

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strain-rate [39]. According to the data in [38], the value of Hall-Petch coefficient increases with increase in strain-rate. According to thermally-activated analysis of the 444 -stress

for fcc materials in [33], this value depends on strain-rate similar to the yield

stress in equation (3): τIII /G~τIII (0K)/G-ln (const/γ0. This gives the same trend in strain444 -stress

as in work of Armstrong and Panin [37,38].

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rate dependence of the

Nevertheless, according to data in Figure 3 and Table 5 kHP-values almost do not vary with strain-rate. This could be associated with power dependence of coefficient ⁄

on strain rate (Fig. 3d), which is weaker as compared to strain-rate

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~ 'ln 1⁄ε0

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dependence of the friction stress (equation 3). As it was measured using TEM, both steels possess low stacking fault energies:

33.6±4.5mJ/m2 for 316SS and 20.6±1.7mJ/m2 for 321SS. At low strain, a planar dislocation arrangement is observed for both steels (Fig. 4), and plastic deformation realizes by dislocation slip. Figure 4 shows that regardless of stacking fault energy and strain rate, the plastic flow of steels near the yield strength is slip-dominated process. But there are some differences in microstructure of the steels. 316SS has higher stacking fault energy than that for 321SS, so planar dislocation arrangement is

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ACCEPTED MANUSCRIPT characteristic for different strain rates and wide stacking faults are rarely observed in TEM images (Fig. 4 a,b). At the same time, wide stacking faults, splitted dislocations and perfect dislocations are clearly seen in TEM images of 321SS-specimens (Fig. 4

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c,d). These microstructural differences could determine the difference in σ0 and values for both steels.

Perfect dislocations a/2<110> in fcc structure are prone to dissociation into two

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partial Shockley dislocations a/6<112> joined by ribbon of stacking fault [40]. This dissociation or splitting is peculiar for alloys and steels with low stacking fault energies

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and is precursor for mechanical twinning. The width of the splitting is inversely dependent on stacking fault energy and could rise/decrease in stress field [41]. Thus, variation in splitting value could determine the elastic interaction of dislocation with solute atoms and ‘forest’ dislocations describing by equation (3). For 321SS with lower

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stacking fault energy, this splitting could be high enough and partial dislocations a/6<112> interact with elastic fields of solute atoms and ‘forest’ dislocations. For 316SS with higher stacking fault energy, the splitting is lower and perfect dislocations

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interact with elastic barriers. As elastic interaction is proportional to the Burgers vector of the dislocation [33,40], the friction stress should be lower for 321SS, in which

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<<<=; = >⁄√6=0.147nm move, than that for splitted dislocations with Burgers vector ;321SS with perfect dislocations ;-<=; = >⁄√2=0.254 nm. This difference in value of Burgers vectors of splitted and unsplitted (perfect) dislocations explains the experimentally observed difference in values of σ0 for the steels (Table 5). The difference in dislocation arrangement could be also responsible for difference in

values for the steels. According to consideration of Armstrong and

Panin [37,38], stress

с

is related to the

444 -stress.

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The value

444

corresponds to the

ACCEPTED MANUSCRIPT beginning of stage III of strain hardening and is strongly dependent on cross-slip ability of the alloy. The

444 -value

is higher for alloys with low stacking fault energies because

cross-slip process is suppressed for them as compared to alloys with high stacking fault A -value

is lower for 316SS as compared to

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energies. Due to the difference in SFE,

value is higher for the steel with lower value of SFE.

321SS and, consequently,

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4. Conclusions

Using thermal-mechanical treatments, specimens with different grain sizes were

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produced for two Cr-Ni-based austenitic stainless steels with different stacking fault energies (analogues of AISI 316L and AISI 321 steels). The effect of grain size and strain-rate on the tensile deformation behavior and strength properties was evaluated for these steels. The following were concluded from the observations. In given grain size interval, (3–73)µm for 316 steel and (0.2–32)µm for 321

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(i)

steel, dependence of the yield strength Petch relationship

.

=

+



.

on the grain size D obeys the Hall-

with high correlation coefficient.

Stress σ0 is strain-rate sensitive value. It increases in 15% and 32% respectively

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(ii)

for 316SS and 321SS with increase in strain rate from 1.0×10-4 s-1 up to 1.0×10-2

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s-1. Apparently, this fact is associated with the dependence of friction stress on

thermally activated short range interaction of dislocations (perfect or partial) with solute atoms and ‘forest’ dislocation, which, in turn, depends on strain rate.

(iii)

Hall-Petch coefficient kHP weakly changes with the strain rate: 322-327 MPa×m0.5 for 316 steel and 404-413 MPa×m0.5 for 321 steel (in the considered strain rate interval 1.0×10-4 s-1 to 1.0×10-2 s-1). One of the reasons of this is weak

square root dependence of kHP value on the strain rate.

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ACCEPTED MANUSCRIPT (iv)

The Hall-Petch coefficient kHP depends on steel composition (stacking fault energy) and possesses higher values for 321 steel as compared to 316 steel. The reason for this is strong influence of stacking fault energy on the shear stress

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value, which is need for of activation of dislocation sources near grain boundaries.

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Acknowlegments

This work was performed within the frame of the Fundamental Research

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Program of the State Academies of Sciences for 2013-2020, line of research III.23.2.7.

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this

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of microstructural evolution in 304L austenitic stainless steel warm deformed by cyclic channel die compression, J. All. Comp. 669 (2017) 1036-1048. [18] Y. Mine, N. Horita, Z. Horita, K. Takashima, Effect of ultrafine grain refinement

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[19] K. Kako, W. Kawakami, J. Ohta, M. Mayuzumi, Effect of various alloying elements on tensile properties of high-purity Fe-18Cr-(14-16)Ni alloys at room temperature. Mater. Trans. 43(2) (2002) 155-162. [20] J.W. Cristian, S. Mahajan, Deformation twinning. Progr. Mater. Sci. 39 (1995) 1157. [21] B. Bal, B. Gumus, G. Gerstein, D. Canadinc, H.J. Maier, On the micro-deformation mechanisms active in high-manganese austenitic steels under impact loading. Mat. Sci.

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ACCEPTED MANUSCRIPT Eng. A. 632 (2015) 29-34 [22] P.B. Hirsch, A. Howie, R.B. Nicholson, D.W. Pashley, M.J. Whelan. Electron microscopy of thin crystals, Butterworths, London, 1965.

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austenitic steel Fe–17Cr–13Ni–3Mo, AIP Conf. Proc. 1683 (2015) 020149-1-020149-4. [25] K. Tomimura, S. Takaki, S. Tanimoto, Y. Tokunaga, Optimal chemical composition in Fe-Cr-Ni alloys for ultra grain refining by reversion from deformation induced martensite. ISIJ Int. 31(7) (1991) 721-727.

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[36] R.W. Armstrong, theory of the tensile ductile-brittle behavior of polycrystalline h.c.p. materials, with application to beryllium. Acta metal. 16 (1968) 347-355. [37] R.W. Armstrong, P. Rodriguez, Flow stress/strain rate/grain size coupling for fcc

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nanopolycrystals. Philos. Mag. 86(36) 2006 5787-5796 [38] V.E. Panin, R.W. Armstrong, Hall–Petch analysis for temperature and strain rate

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dependent deformation of polycrystalline lead. Phys. Mesomech. 19(1) (2016) 35-40. [39] F.J. Zerilli, R.W. Armstrong. Dislocation-mechanics-based constitutive relations for material dynamics calculations. J. Appl. Phys. 61(5) (1987) 1816-1825 [40] D. Hull, D.J. Bacon, Introduction to dislocations. Fifth edition, Elsevier, UK, 2011. [41] S.M. Copley, B.H. Kear, The dependence of the width of a dissociated dislocation on dislocation velocity. Acta Met. 16(2) (1968) 231-237.

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ACCEPTED MANUSCRIPT Figure and Table captions Table 1. Comparative analysis of Hall-Petch coefficient kHP values for different AISI 3XX-type steels subjected to uniaxial tensile tests at room temperature

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Table 2. Chemical composition of the steels (mass.%) Table 3. Regimes of thermal-mechanical treatment and resultant grain sizes (excluding twin boundaries) in 316SS and 321SS

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Table 4. Tensile properties and the initial volume fraction of α’-phase (ϕα’) in 316 and 321 austenitic stainless steels with different grain sizes

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Table 5. Experimentally evaluated parameters of Hall-Petch relationship for 316 and 321 steels tensile tested at different strain rates

Figure 1. Characteristic LM (a) and EBSD (c) images of grain structure and engineering stress-engineering strain curves (b,d) for 316SS: (a,b) – 316_1050/5, grain size 63.9 µm;

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(c,d) 316_950/5, grain size 2.76 µm.

Figure 2. Characteristic EBSD (a,c) and TEM (e) images of grain structure and engineering stress-engineering strain curves (b, d, f) for 321SS: (a,b) – 321_1050, grain

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size 15.1 µm; (c,d) 321_950, grain size 2.7 µm; (e,f) 321_650, grain size 0.2 µm. Figure 3. The variation of the yield strength σ0.2 with grain size (D-1/2) for 316SS (a) and

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321SS (b) specimens obtained for different strain rates; dependencies of σ0 on ln'1⁄ 0 (c) and Hall-Petch coefficient on 'ln 0



(d) for both steels.

Figure 4. Bright-field TEM images of dislocation arrangement in coarse-grained 316SS (a, b) and 321 SS steel (c, d) after uniaxial tensile test up to 5% plastic strain: (a, c) strain rate 1×10-4 s-1; (b, d) strain rate 1×10-2 s-1. Grain sizes are 16 µm for 316 SS and 32 µm for 321 SS.

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ACCEPTED MANUSCRIPT Table 1. Comparative analysis of Hall-Petch coefficient kHP values for different AISI 3XX-type steels subjected to uniaxial tensile tests at room temperature ε, s-1

Treatment type

AISI316L [1] AISI 316 L [11]

Rolling at Т=773-1173К Rolling at room temperature with subsequent annealing Heat treatment Annealing at 1173 and 1573K Thermomechanical treatment Thermomechanical treatment Thermomechanical treatment Multidirectional forging

1×10-4

Rolling at room temperature and at 573K with subsequent annealing Laser-based directed energy deposition Cyclic channel die pressing technique High-pressure torsion

AISI 316L-P [14] AISI 316L [14]

AISI 304L [16] AISI 304L [17]

247.9

3×10−4

26-230

330.7

3×10−4

2.8-73

314.9

2.5×10−3

0.04-0.1

220

3×10−3

0.1-163

470

1.2×10−3

31-81

695

-

0.04-150

398

2×10−3

0.1-0.5

450

-

0.05-0.5

395

-

~1.6-26

~522

2×10−3

0.22-25.3

363

4.2×10−3

7.7-115.5

403-505

Heat treatment

4.2×10−3

6.3-70.9

537

Heat treatment

4.2×10−4

5.7-94.7

302-365

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Fe-17Cr-6Ni austenitic stainless steel [8] Fe-18Cr-14Ni(Si, Mn, C, P, S) type steel [19] Fe-18Cr-14Ni0.1N [19] Fe-18Cr-16Ni-(02)Mo [19]

30-80

Rolling at room temperature with subsequent annealing Cold rolling and following heat treatment (annealing) Severe cold deformation and reverse-transformation annealing Heat treatment

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AISI 304-type [18] AISI S304H [2]

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AISI SUS316 [15] AISI 304L [5]

AISI 304 [6]

3×10−4

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AISI 316L-I [14]

– 1×10-4

0.85-3.4 3.1-10 10-86.7 30-138 3.1-86.7

kHP, MPa× µm 0,5 412 501 131 ~474 279.95

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AISI 316 [12] AISI 316L [13]

D, µm

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Steel type

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Cr 16.8 17.7

13.3 9.8

2.7 0.2

– 0.6

1.7 1.3

0.6 0.5

0.01 0.11

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Steel Fe type 316SS Balanced 321SS Balanced

Table 2. Chemical composition of the steels (mass.%) Ni Mo Ti Mn Si С

Table 3. Regimes of thermal-mechanical treatment and resultant grain sizes (excluding

316SS

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321SS

Thermal-mechanical treatment regime SST о SST→CR→1050 С-annealing for 4 hrs SST→CR→1050оС-annealing for 5 hrs SST→CR→950оС-annealing for 5 min SST→CR→950оС-annealing for 10 min SST SST→CR→1050оС annealing for 5 hrs SST→CR→950оС annealing for 3 min SST→CR→750оС annealing for 10 min SST→CR→650оС annealing for 30 min

Notation key 316_I 316_1050/4 316_1050/5 316_950/5

Grain size, µm 16.40±8.75 73.20±3.08 63.9±30.66 2.76±1.14

316_950/10

6.08±2.57

321_I 321_1050 321_950 321_750 321_650

31.83±10.95 15.10±11.70 2.74±1.40 0.70±0.63 0.21±0.09

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Steels

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twin boundaries) in 316SS and 321SS

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Table 4. Tensile properties and the initial volume fraction of α’-phase (ϕα’) in 316 and 321 austenitic stainless steels with different grain sizes Material, Strain rate Yield strength Tensile Elongation ϕα’, % -1 treatment (σ0.2), MPa strength (δU), % ( ), s (σUTS), MPa 316_I 1×10-4 341±7 973±6 59±2 0 -3 1×10 352±5 1083±7 73±2 1×10-2 368±6 1031±6 62±3 -4 316_1050/4 1×10 280±5 862±6 44±3 0 1×10-3 295±7 990±5 55±2 1×10-2 322±7 972±8 56±2 316_1050/5 1×10-4 282±7 968±8 54±1 0 -3 1×10 291±5 1018±6 59±3 -2 1×10 320±6 977±10 52±3 316_950/5 1×10-4 437±9 915±11 34±1 0 -3 1×10 452±10 958±14 37±2 1×10-2 476±8 942±9 36±1 316_950/10 1×10-4 382±10 952±10 42±2 0 1×10-3 389±9 940±9 39±1 1×10-2 411±9 997±10 45±2 -4 321_I 1×10 190±5 927±7 69±3 2.4±0.12 1×10-3 202±4 939±5 69±2 1×10-2 212±7 906±8 65±3 321_1050 1×10-4 186±4 946±6 58±2 0.1±0.05 -3 1×10 198±6 1021±7 68±2 1×10-2 208±8 952±5 58±3 321_950 1×10-4 341±8 855±7 33±1 2.0±0.1 -3 1×10 370±7 955±7 38±1 1×10-2 409±4 960±5 42±2 -4 321_750 1×10 855±9 1141±10 10±2 1.6±0.08 1×10-3 985±8 1118±9 8±1 1×10-2 900±10 1125±12 7±2 321_650 1×10-4 972±8 1242±13 6±1 4.1±0.2 -3 1×10 989±8 1262±9 8±1 -2 1×10 1021±10 1240±12 6±2

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Table 5. Experimentally evaluated parameters of Hall-Petch relationship for 316 and 321 steels tensile tested at different strain rates -1 kHP, MPa×m0.5 Steel type R ,s , MPa 10-4 246 325 0.98 10-3 257 327 0.99 316SS 10-2 283 322 0.98 -4 10 100 404 0.99 321SS 10-3 116 409 0.99 -2 10 132 413 0.99

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Figure 1. Characteristic LM (a) and EBSD (c) images of grain structure and engineering stress-engineering strain curves (b,d) for 316SS: (a,b) – 316_1050/5, grain size 63.9 µm;

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(c,d) 316_950/5, grain size 2.76 µm.

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Figure 2. Characteristic EBSD (a,c) and TEM (e) images of grain structure and engineering stress-engineering strain curves (b, d, f) for 321SS: (a,b) – 321_1050, grain size 15.1 µm; (c,d) 321_950, grain size 2.7 µm; (e,f) 321_650, grain size 0.2 µm.

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Figure 3. The variation of the yield strength σ0.2 with grain size (D-1/2) for 316SS (a) and 321SS (b) specimens obtained for different strain rates; dependencies of σ0 on ln'1⁄ 0 (c) and Hall-Petch coefficient on 'ln 0 ⁄ (d) for both steels.

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Figure 4. Bright-field TEM images of dislocation arrangement in coarse-grained 316SS (a, b) and 321 SS steel (c, d) after uniaxial tensile test up to 5% plastic strain: (a, c) strain rate 1×10-4 s-1; (b, d) strain rate 1×10-2 s-1. Grain sizes are 16 µm for 316 SS and 32 µm for 321 SS.

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